Geometry 2.3.1 Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What is the minimum length of the third side if two sides of a triangle are 7 cm and 10 cm?

Back

The minimum length of the third side must be greater than 3 cm (10 - 7).

Front

What is the maximum length of the third side if two sides of a triangle are 7 cm and 10 cm?

Back

The maximum length of the third side must be less than 17 cm (7 + 10).

Front

If one side of a triangle is 12 cm and the other two sides are 5 cm and x cm, what is the range of possible values for x?

Back

x must be greater than 7 cm and less than 17 cm.

Front

What is the relationship between the angles and sides in a triangle according to the Triangle Inequality Theorem?

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

How can the Triangle Inequality Theorem be used to determine if three lengths can form a triangle?

Back

By checking if the sum of any two lengths is greater than the third length.

Front

What is an example of three lengths that cannot form a triangle?

Back

Lengths 1 cm, 2 cm, and 3 cm cannot form a triangle because 1 + 2 is not greater than 3.

Front

What is the significance of the Triangle Inequality Theorem in real-world applications?

Back

It helps in determining the feasibility of constructing triangular structures, such as roofs and bridges.

Front

If a triangle has sides of lengths 8 cm, 15 cm, and 20 cm, does it satisfy the Triangle Inequality Theorem?

Back

No, because 8 + 15 is not greater than 20.